Category Archives: Number

268. Monkeying with Pythagoras

My (not so little) monkeys in KS3 have been discovering and using Pythagoras’ Theorem. They usually deal with open questions quite well, however this one took a fair bit of discussion. This challenge requires no worksheets or fancy resources, just write it on the board. The context is modified, but the essential question remains the same.

Challenge

Zookeepers have attached eight bolts in a cuboid formation (sides 3m, 4m and 5m) to the trees in a chimpanzee enclosure. The keepers attach taut ropes between the bolts for the chimps to climb on. Each length of rope is individually cut. No length is lost in knots.

  • What is the maximum length of any one piece of rope?
  • What is the total amount used, if every corner is joined without duplication?

 

Solution

The first step to solving it is a good diagram of the problem. Students then need to break it down into triangles. The solution has several levels of difficulty:

  • Total of the edges of the cuboid
  • Total of the diagonals on the faces
  • Total of the diagonals across the inside of the cuboid

This diagram demonstrates the levels of the problem – have fun!
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263. Percentages Tick or Trash

To quote a famous DIY company from the UK, this post ‘Does exactly what it says on the tin’!

ronsealImage credit: www.ronseal.co.uk

Here is a tick or trash worksheet on percentages, including a couple of tricky ones:

Percentages Tick or Trash inc solution

I usually tick these worksheets until I find a mistake. I then tell the student to have a rethink. Obviously the correct answer is the other option, but the working out will need to be corrected. I also do not tell them how many of the remaining questions are actually correct – they then recheck these before I mark it again.

The only difference with this worksheet is that students have space for working out – no more guessing! The extension task asks students to try and figure out where the wrong (misconception) answers come from – that can be quite tricky and tests their understanding.

262. Percentage Building Blocks

A quick reverse percentages resource for you. I explain reverse percentages by using both calculations and diagrams. These resources can be used as a starter activity or as a selective discussion point. The presentations are editable and the pdf is identical to them. I hope they are useful in addressing the reverse percentages misconceptions!

Reverse Percentage Problem (pdf)

Reverse Percentage Problem (ppt)

Reverse Percentage Problem (pptx)

261. Revision Egg Hunt

It’s beginning to look a lot like Easter … scrawny plastic chicks and over-priced chocolate eggs everywhere! This little ‘egg’ of an idea was totally inspired by some lovely Tweeters who mentioned ways to use empty plastic eggs.

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Equipment
I bought these two-part plastic eggs from a local craft shop. They are available from lots of places on the high street and online. My pack has 30 eggs in six different colours. You may be able to see that I’ve numbered the top and bottom of each shell – just to avoid arguments.

Activity
Now, I used these eggs for revision with my GCSE class. Each colour represents a different topic. There are 30 questions and the answers are the numbers 1 to 30. I hid the eggs in our main hall due to the unpredictable nature of the British weather. You could hide them inside or outside the classroom and give a prize to the person/group who correctly completes the most questions. Points could be deducted for trying to sabotage other groups. If you don’t feel that adventurous or it’s impossible to go outside, you could copy the questions and do this as a desktop activity.

Topics
Sometimes we get tunnel-vision on the focus for passing exams. We keep the ‘fun’ stuff for younger pupils. This revision activity is a treat for my hard-working students in KS4. They aren’t the easiest of topics, but they are perfect for students working at GCSE grade C and above.

1-5 Expanding & factorising quadratics
6-10  Ratio & Proportion
11-15  Straight line graphs (y=mx+c)
16-20  Simultaneous Equations
21-25  Shape problems
26-30 Factors & Multiples

Resource
You can download the questions here: Easter revision 30Q
You can download the solution here: Easter revision 30Q Solutions

Feedback
I was surprised to get feedback from this activity from a form teacher, who said their students had arrived at registration bouncing and saying how much they had enjoyed the lesson!

260. Filter Maths

There is a moment of satisfaction to be had when the last drip of filter coffee drops into the jug: a lovely aroma of fresh coffee and the anticipation of a well-earned drink.

coffee-cup

Image Credit: http://vidacoffeeco.com/

Don’t worry, the ‘Sandpit’ hasn’t gone all hipster foodie overnight! The slow drip of coffee leading to a rewarding cup matches perfectly with the slow drip of revision, leading to a rewarding grade.

The exam season is fast approaching and the photocopiers are starting to crank out past papers. You start handing out papers and expect them to hand them in …

That’s the point it starts to go wrong:

  • They don’t hand them in.
  • They give up halfway through.
  • They skip pages and it takes you ages to find what they’ve done.
  • They lose confidence.
  • If you issue A5 size booklets they lose them.
  • If you issue A4 size booklets, they complain and the booklets get mangled.
  • You get frustrated – don’t they realise it’s for their own good!

This year, why not try out this idea instead:

  • Hand out the exam board formulae sheet.
  • Hand out the grade boundaries.
  • Hand out the first four pages reduced to A4, back to back.
  • Collect in the first sheet.
  • Repeat for the next four pages.
  • Collect in the second sheet.
  • Repeat until the questions start getting harder, then decrease it to two pages back to back.
  • Continue until the paper is finished.

This is time-consuming and it is best started well in advance of the main revision period, but it works. The individual sheets have a manageable amount of content and are less intimidating – they also weigh a lot less than 33 exam papers. As a teacher, you get a clear picture of which areas to revisit as the topic list is short. Each student keeps a running total of how they are doing on the paper. The grade boundaries sheet lets them keep track of their progress towards their target grade.

The consequence of doing this process with a couple of papers is that students feel more confident approaching papers. They will start to notice themes in the wording and topics. They will also realise that it’s important to ‘bank’ as many marks as they can in the first half of an exam paper.

My class responded well to this drip-feed of questions. After the first sheet they felt proud of themselves when they realised they’d achieved a grade D in just four pages of a Higher paper and were calculating how many marks they’d need for a C. The number of late homeworks dramatically dropped and the effort level went up.

This idea is simple and non-subject specific. It would work equally well with physics, chemistry, biology … in fact any paper which has a fair number of questions.

Good luck with the revision!

 

 

257. Making the absurd Rational

Here’s a nifty little resource for you, once again inspired by @MrReddyMaths

mathsheart

Image Credit: http://blog.spaldingacademy.k12.ne.us/sa/files/2010/09/math-3.gif

This worksheet takes you through the process of rationalising fractions where the denominator is a surd. All of the numerators are integers to make the focus the denominator.

Updated version of (pdf)

This new version is A4 sized to allow more space for working out.

If you like this, why not try out these:

232. Steps in Volume

241. Histogram Hysteria

 

251. Safe as trees

Here’s a two in one post for you, with a wooden theme:

safecracker

Tree 1

This fascinating wooden puzzle is available on Etsy. Each line has to add up to 50 – simple? Not as easy as you’d think. A perfect classroom extension puzzle or gift for a puzzle fanatic!

Tree 2

A little starter on logarithms, with a touch of safecracking too!

Crack the safe Logarithms

The questions are sourced from an A-Level textbook – why not make your own textbook tasks more interesting by creating your own safecrackers on the board? Five minutes prep = puzzle fun!